Relativistic Quantum Metrology: Exploiting relativity to improve quantum measurement technologies

Abstract

We present a framework for relativistic quantum metrology that is useful for both Earth-based and space-based technologies. Quantum metrology has been so far successfully applied to design precision instruments such as clocks and sensors which outperform classical devices by exploiting quantum properties. There are advanced plans to implement these and other quantum technologies in space, for instance Space-QUEST and Space Optical Clock projects intend to implement quantum communications and quantum clocks at regimes where relativity starts to kick in. However, typical setups do not take into account the effects of relativity on quantum properties. To include and exploit these effects, we introduce techniques for the application of metrology to quantum field theory. Quantum field theory properly incorporates quantum theory and relativity, in particular, at regimes where space-based experiments take place. This framework allows for high precision estimation of parameters that appear in quantum field theory including proper times and accelerations. Indeed, the techniques can be applied to develop a novel generation of relativistic quantum technologies for gravimeters, clocks and sensors. As an example, we present a high precision device which in principle improves the state-of-the-art in quantum accelerometers by exploiting relativistic effects.

Quantum estimation of the Schwarzschild spacetime parameters of the Earth

“…This theoretical framework enables one to incorporate relativistic effects at the low energy regimes that are being reached by cutting-edge quantum experiments. Recently, methods for the application of quantum metrology to quantum field theory have been introduced in [6,7]. Interestingly, relativistic effects such as particle creation, can be exploited to measure accelerations with an optimal measurement precision that is higher than the non-relativistic counterpart [7].…”

A Brief Note on the Clock-Hypothesis

“…While, of course, we compromised in principle by choosing a semi-classical treatment, it seems that, compared to moving particles, atomic clocks are even less ideal devices though, since they are not point-like, and Equation (11) only holds neglecting any real clock components other than the photon-emission/absorption. There might be effects on the photon by other parts of the clocks [9] or a more sophisticated description of the oscillator by a quantum-field might lead to particle-creation [10]. Qualitatively, we can see already from our model, e.g.…”

“…Some recent work focuses on the fact that real clocks are never point-like entities and that consequently forces between its constituent parts or between different clock-devices can influence the duration-measurement at the quantum level. The considerable machinery of quantum-field theory in curved space-time is applied in [9] to describe gravitational effects on the clocks or in [10] to find e.g. an impact of particle-creation on the duration measurement.…”

Quantum estimation of parameters of classical spacetimes

“…There has recently been some promising work in this direction [11][12][13], focusing on quantum probes consisting of scalar fields in Gaussian states. Here we present a general formalism for relativistic quantum metrology, using arbitrary fields and states.…”